TY - JOUR

T1 - On inverse sum indeg energy of graphs

AU - Jamal, Fareeha

AU - Imran, Muhammad

AU - Rather, Bilal Ahmad

N1 - Funding Information:
Funding information: This research is supported by UPAR Grant of United Arab Emirates University (UAEU),Al Ain, UAE via Grants No. G00003739.
Publisher Copyright:
© 2023 the author(s).

PY - 2023/1/1

Y1 - 2023/1/1

N2 - For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.

AB - For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.

KW - adjacency matrix

KW - energy

KW - inverse sum indeg matrix

KW - topological indices

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U2 - 10.1515/spma-2022-0175

DO - 10.1515/spma-2022-0175

M3 - Article

AN - SCOPUS:85144735047

SN - 2300-7451

VL - 11

JO - Special Matrices

JF - Special Matrices

IS - 1

ER -